On a typical week, the Torah is read publicly on Monday, Thursday, and twice on Shabbat. On holidays, fast days, and Rosh Chodesh, the Torah is read regardless of the day of the week.

When did this start?

Moses instituted that the Torah be read three days a week. The Talmudic sages1 find this alluded to in Exodus (15:22-27), where we read that our ancestors traveled for three days and thirsted for water—which allegorically also refers to the Torah. They had become spiritually ill after not studying Torah. In response, Moses and the prophets of his generation decided that three days should never pass without a public Torah reading. Thus, we read the Torah on Shabbat, then skip a day and read it on Monday, then skip two days and read it again on Thursday—then two days later we are back at Shabbat.2

At first glance, this would seem to contradict the tradition3 that Ezra the Scribe and the Men of the Great Assembly introduced the practice of reading the Torah on Mondays and Thursdays in the 4th century BCE.

The Talmud reconciles these two traditions by explaining that they refer to different stages in the evolution of this tradition. In Moses' times only three verses were read (corresponding to the three general groups within the Jewish community: Kohen, Levi, and Yisrael) on the weekdays. Ezra and associates lengthened this quota to a minimum of 10 verses (divided into three Aliyot).

Please let me know if this helps.

Yours truly,

Rabbi Baruch S. Davidson